


Number Man Does His Taxes

by babagaia



Series: Quod Eroticat Demonstrancum [1]
Category: Parahumans Series - Wildbow
Genre: Mathematics
Language: English
Status: Completed
Published: 2018-07-28
Updated: 2018-07-28
Packaged: 2019-06-17 13:20:35
Rating: Teen And Up Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 1,574
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/15462273
Author URL: https://archiveofourown.org/users/babagaia/pseuds/babagaia
Summary: Betaed by Chartic, MOXCRunner1, and Pericardium. Thank you for corrections, advice, and encouragement.





	Number Man Does His Taxes

**Author's Note:**

  * For [xbritomartx](https://archiveofourown.org/users/xbritomartx/gifts), [CPericardium](https://archiveofourown.org/users/CPericardium/gifts).



(Cover by [CPericardium](https://archiveofourown.org/users/CPericardium/). Check out [her art](http://deviantart.com/cpericardium/)! And her [Number Man featuring fic!](https://archiveofourown.org/works/13796073/))

 

“I heard number man has a big dick.” — maroon_sweater (02/15/2018)

***

“Number Man! You got a minute?”

“No!”

“The property bubble in Japan just burst! We need—”

“I said no!”

“What are you doing?”

“Our finances.”

“Again? This is the third time today!”

“The global financial situation is fickle. When the need arises, I have to attend to it. Now go away! You’ll have to manage without me.”

He started pacing faster. Movement was important; it helped get the blood flowing and might get him back into the right mood. His thoughts turned to what he was manipulating. This was a tricky problem, a tough nut.

Number Man was no amateur. He’d honed his craft over long days and nights working through similar problems while hiding from parents, peers, and coworkers. Where a novice might look at a tax form and see a tree of checkboxes culminating in a simple sum, he saw deep structure: groupoids shriveling to finity, hilbert spaces of countable measure, type systems inconsistent with modus ponens.

Abstraction.

Everything lives in an appropriate category. Figure out which are the arrows and which are the objects, and all that’s left is to follow the morphisms.

The beginning was always slow. Feel out the space, experiment a little, try to twist the problem into shape.

Nothing called to him. Weak solution attempts led to fleeting threads. He pulled on them weakly, trying to find anything to lead him down the right path, lead him into that domain of pure, unstoppable reason.

He’d have to get more creative.

He followed a natural transformation into a geometric frame of reference. His mind’s eye traced imaginary curves. They simplified into graphs that danced and jiggled in his thoughts. He considered the girth. It wasn’t general enough. He could lower that bound and tighten the loop if he applied this rather gripping postulate.

Sometimes, to solve an especially difficult problem, he had to get weird. Freaky even. He’d delved into realms of mathematics that nobody wants to stumble into without warning: degenerate cases, topological counterexamples, non-measurable sets.

Some mathematicians needed reference books full of images. They’d pore over them, carefully examining diagram after diagram, hoping for that tug on their imagination, until they found something that clicked.

For others, pictures didn’t do much. Laid out in static ink, they lacked all the details that a well-crafted proof held. A figure might hold the core idea, the final concept necessary for completion, but it lacked all the buildup, all the little details that went into ensuring soundness and consistency.

Number Man was a rare breed. For all the work he did, he rarely ran past the bounds of his own imagination. Through long hours of thoroughly enjoyable practice, he’d built up a library of topics to peruse. Everything was in his head. Modern mathematics for all its vaunted complexity couldn’t hope to break him.

He wandered through the halls of his own mind, contemplating and searching for some idea to pull on.

There it was: a simple transformation rid him of metrizable cruft and left only the relevant topological underpinnings. An injective mapping simplified it further. Applying a pullback, he followed up with a pushforward of the vector bundle.

Yank it back into the original space, and that’s a lemma.

Subproof in hand, he was closer than ever. The excitement of having made a step forward lubricated the mental tracks he was following and spurred him on, implications coming faster now.

He’d originally expected a problem with the jerk, but this was turning out quite smooth. He integrated along the fiber. The vector bundle was tight, pulsing with information, connected via surjective map to another total space. With the dimension lowered, the entire thing seemed to solidify.

Another breakthrough: the morphisms he was interested in were epis.

That was useful, but not enough. If he could show that–

Another voice intruded on his diligent efforts, muffled by the door to his office. “Number Man, are you free yet?”

He stumbled mid-thought, losing track of his reasoning. “I'm working through some very important calculations!” He glanced down. “The numbers are getting rather large, hard for even me to handle, so stop distracting me.”

Footsteps trailed off into the distance.

The previous bit of logic now lost to him, he considered the problem from a different angle.

By tracing the continuities of the original space, he reworked everything into a deceptively simple looking set of equations. They provably peaked at important properties, but failed to give up their secrets in response to algebraic prodding.

Were he lesser, he may have run them iteratively through a computer, but with his power it was trivial to apply numerical techniques himself. Simple cases revealed nothing. The complexity of his attempts increased rapidly, soon outpacing his ability to keep up, forcing him to massage the numbers more and more to get anything out of them.

Map an element, invert. Checking the result, he was unsatisfied. Map, invert. Better to try again—better to have a larger sample. Map, invert.

Traversing the space correlated with increasing stiffness ratios.

Instability abounded. Pursuing this would lead either directly to the answer or be a messy waste of time.

Roundabout methods always existed. In his youth, he’d often tried the same approach over and over with only minor variations, held onto flawed ideas too tightly, pushed and pulled and refused to budge from some narrow preconception. Even when it worked, it was aggravating, a frustrating climb up a sheer cliff face from which he could be dislodged at any moment. At the top, he might find a solution, but he’d be left with a rash of the mind, an irritation of empty, samey math.

Gambles only had to pay off in expectation to be worth more than that hell of monotony.

Given the results of his numerical explorations, he considered the sphere bundle. He kneaded and twisted the geometry, feeling out the inherent structure.

A probabilistic correspondence!

Applying the relevant transform to a standard mixture, he ended up with a sawtooth wave. He winced. That pinched the data to too low a dimension.

What if he considered this linear surjection?

Brain swollen with applicable identities, he forged on. Excited and impatient, he abandoned generality and gave in to force. A painfully convoluted bit of logic led him to another milestone: the epis were isos.

With that equivalence, the real fun began.

This diagram commuted, so he pulled it all back. Multiple domains now caught in his web, he could exploit his expanded toolbox and speed up. He was almost there, but he needed something even more inspiring to guide him to the finish. He couldn’t stop now.

Following a gradient upwards, he let out a sigh of satisfaction as the function stayed monotonic. With a quick inverse, he transformed and simplified the object he was interested in, its thickness becoming clear, its degeneracy even clearer.

He could deform that with some geometric flow, oscillate the shape to get the desired result. Expand some regions, contract others. Follow the motion until it could go no further. Apply the equivalence. Feel out the contour. Reduce. The diagram commutes. Pull it all back. It’s a tensor space. Take the quotient.

It was all coming to a head. Every thread converging to the same argument. He could almost see it. Just one more transformation. Examine the homology. Pullback. Q.E.D.

The throbbing in his temples reflected the throbbing in his mathematics.

Logic lay bare before him. Final connections sparked, thoughts pumped up from the depths of his subconscious and sloshed together until they coalesced into messy globs of core ideas. Complex calculations unwound into rigid formality.

No more difficult thinking or desperate searching. All that was left was letting it all out, and watching it come together into a simpler whole.

The structure now evident, corollaries shot out in irregular spurts, his thoughts lurching as he shuddered in the ecstasy of proof. A final musing solidified into a single coherent whole, and he was left empty.

That was it.

He stopped pacing and leaned back, relaxing and letting the feeling of completion wash over him.

Equations sprawled across the walls. Jotted down in those final moments of enlightenment, they may as well have been splattered on, tendrils of math reaching up to the ceiling and dripping onto the floor. So taken by the moment, Number Man hadn’t stopped to consider where he was writing.

He was done, but only for now. A proof that so thoroughly changed his thinking was going to be sticky. It would cling to his mind, flashes of reasoning and snippets of structure bubbling up in his thoughts later on. If he didn’t pursue, didn’t come back and spend some time proving further propositions, they’d fester. They’d weigh on his mind, become a pressure in his head that invaded his every thought and distracted him from other work.

Someone banged on the door to his office. “Situation in Algiers!”

“One more minute!”

“We don’t have time for this, Number Man!”

“Alright, alright.”

He wiped his hands on the wall towel and fixed his suit.

The door opened and Contessa poked her head in, glancing around at the mess in his office. She smirked. “How did the finances go?”

As they left, Custodian began the futile, never-ending task of cleaning up after Number Man.

**Author's Note:**

> Betaed by Chartic, MOXCRunner1, and Pericardium. Thank you for corrections, advice, and encouragement.


End file.
